Haskell's lazy evaluation makes it easily possible to coinductively specify, and compute, infinitary structures such as streams. In particular, the coinductive stream calculus can easily be implemented using simple Haskell code, and there is a close relationship between systems of behavioural differential equations for streams on one side, and coinductive …

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# The Coinductive Stream Calculus

We will consider coalgebras of the type $F(X) = mathbb{R} imes X$, representing streams over real numbers. For such streams, we coinductively define a number of operators (including, but not limited to, addition and multiplication), and we furthermore consider coinductive proofs through bisimulation. We will discuss polynomial and rational …

read more# An Introduction to Coalgebra and Coinduction, using Regular and Context-free Languages

We give a summary of some of the existing work on coalgebra and coinduction: a general introduction to the coalgebraic framework is given, focussing especially on the instance of coalgebraic representations of regular and context-free languages, and deterministic automata. We show how Brzozowski derivatives of regular expressions fit into the …

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